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We show that the Hawking--Penrose singularity theorem, and the generalisationof this theorem due to Galloway and Senovilla, continue to hold for Lorentzianmetrics that are of $C^{1, 1}$-regularity. We formulate appropriate weakversions of the strong energy condition and genericity condition for$C^{1,1}$-metrics, and of $C^0$-trapped submanifolds. By regularisation, weshow that, under these weak conditions, causal geodesics necessarily becomenon-maximising. This requires a detailed analysis of the matrix Riccatiequation for the approximating metrics, which may be of independent interest.

The Hawking-Penrose singularity theorem for $C^{1,1}$-Lorentzian metrics